Editing Zipf's law (section)

==History==
In 1913, the German physicist [[Felix Auerbach]] observed an inverse proportionality between the population sizes of cities, and their ranks when sorted by decreasing order of that variable.<ref name=Auerbach1913/>

Zipf's law had been discovered before Zipf,{{efn|as Zipf acknowledged<ref name=zipf1949/>{{rp|546}}}} first by the French stenographer [[Jean-Baptiste Estoup]] in 1916,{{refn|
{{cite book |first=J.-B. |last=Estoup |author-link=Jean-Baptiste Estoup |year=1916 |title=Gammes Stenographiques |edition=4th }} Cited in {{harvp|Manning|Schütze|1999}}.<ref name=mann1999/>
}}<ref name=mann1999/> and also by [[Godfrey Dewey|G. Dewey]] in 1923,<ref>{{cite book |last=Dewey |first=Godfrey |year=1923 |title=Relative Frequency of English Speech Sounds |publisher=Harvard University Press |url=https://archive.org/details/in.ernet.dli.2015.18294 |via=Internet Archive }}</ref> and by [[Edward Condon|E. Condon]] in 1928.<ref>{{cite journal |last=Condon |first=E.U. |author-link=Edward Condon |year=1928 |title=Statistics of vocabulary |journal=[[Science (journal)|Science]] |volume=67 |issue=1733 |page=300 |doi=10.1126/science.67.1733.300 |pmid=17782935 |bibcode=1928Sci....67..300C }}</ref>

The same relation for frequencies of words in natural language texts was observed by George Zipf in 1932,<ref name=zipf1935/> but he never claimed to have originated it. In fact, Zipf did not like mathematics. In his 1932 publication,<ref name=zipf1932/> the author speaks with disdain about mathematical involvement in linguistics, ''a.o. ibidem'', p.&nbsp;21:
: ''... let me say here for the sake of any mathematician who may plan to formulate the ensuing data more exactly, the ability of the highly intense positive to become the highly intense negative, in my opinion, introduces the devil into the formula in the form of'' <math>\ \sqrt{ -i\; } ~.</math>
The only mathematical expression Zipf used looks like {{nobr|{{math|''ab''<sup>2</sup>}} {{=}} constant,}} which he "borrowed" from [[Alfred J. Lotka]]'s 1926 publication.<ref name=king1942/>

The same relationship was found to occur in many other contexts, and for other variables besides frequency.<ref name=piant2014/> For example, when corporations are ranked by decreasing size, their sizes are found to be inversely proportional to the rank.<ref name=axte2001/> The same relation is found for personal incomes (where it is called [[Pareto distribution#Occurrence and applications|Pareto principle]]<ref>{{cite book |doi=10.1016/B978-0-444-59428-0.00002-3 |title=The Principal Problem in Political Economy |series=Handbook of Income Distribution |date=2015 |last1=Sandmo |first1=Agnar |volume=2 |pages=3–65 |isbn=978-0-444-59430-3 }}</ref>), number of people watching the same TV channel,<ref name=erik2014/> [[musical note|notes]] in music,<ref name=zann2004/> cells [[transcriptomes]],<ref name=lazz2023/><ref name=chen2011/> and more.

In 1992 bioinformatician [[Wentian Li]] published a short paper<ref name=liwe1992/> showing that Zipf's law emerges even in randomly generated texts. It included proof that the power law form of Zipf's law was a byproduct of ordering words by rank.